Germany, Spain, France, Britain and Sweden are among the European countries that decided Monday to endorse Guaido and his call for a new round of presidential race in the country.
Guterres was encouraged by last Saturday's peaceful protest, saying "Our strong call is to avoid all forms of violence, that, of course, have no objective and do not benefit anyone".
The young lawmaker accused the military on Monday of planning to divert aid being stockpiled in Colombia, Brazil and an unidentified Caribbean island, in order to distribute it through the socialist government's subsidized food program for its own supporters.
Saturday saw rival protests as tens of thousands of people demonstrated in Caracas, some demanding Maduro's resignation and others celebrating 20 years since Maduro's mentor, Hugo Chavez, came to power.
Tensions have mounted in the South American nation with Maduro refusing the opposition's calls to step down.
Guaido appealed to the military's "conscience" to let the aid reach those most in need.
Guaido knows he needs the armed forces on his side to dislodge Maduro.
Mexico and Uruguay had hoped that UN Secretary-General Antonio Guterres would attend a conference in Montevideo on Thursday aimed at promoting dialogue between Venezuela's self-proclaimed President Juan Guaido and leader Nicolas Maduro.
Guterres said he was following the crisis in Venezuela "with a lot of concern", adding that he had discussed the various initiatives put forward with the countries involved. "The kind of democracy which political protesters in Canada do enjoy and, I am sad to say, political protesters in Venezuela do not".
The U.S. has led an global campaign to put economic and diplomatic pressure on Maduro, including the imposition of sanctions on the country's state-owned oil company.
Eurasia said United States oil sanctions are "set to have a broad impact" with the government facing "the prospect of running out of gasoline, which could serve as another social catalyst".
The Canadian Union of Public Employees (CUPE) - Canada's largest union - the Canadian Union of Postal Workers and the Canadian Labour Congress have expressed varying degrees of concern over Canada's move to recognize Guaido as interim president. Washington has repeatedly demanded that Maduro should resign from his post. "We have to come to buy food because we can not even get cooking oil and eggs in Venezuela".
Guaido says the May 2018 vote in which Maduro won a second term was a sham and on January 23 invoked a constitutional provision to declare himself president, promising free and fair elections.
The Lima Group of Latin American countries and Canada called Monday for a peaceful change in government in Venezuela, without military intervention.